Factor each polynomial by grouping the first two terms and the last two terms. x^3-4x^2+2x-8?

Question

Factor each polynomial by grouping the first two terms and the last two terms. x^3-4x^2+2x-8

Answer 1

*You don't always have to group the very 1st terms. In this case, you could also group the 1st & 3rd term together.

First: group "like" terms.

(x^3 + 2x) - (4x^2 - 8)

Sec: factor both sets of parnethesis.

x(x^2 + 2) - 4(x^2 + 2)

Third: make sure the terms in parenthesis are the same - combine the inner term (once) with the outer term.

(x - 4)(x^2 + 2) or, (x^2 + 2)(x - 4)

Answer 2

x^3-4x^2+2x-8
Group the first two terms:

x^3 - 4x^2
x^3 is the same as x times x^2, so we can rewrite

x x^2 - 4 x^2
x^2 is common to both:
x^2 (x - 4)

Group the last two terms:
2x - 8
8 is 2 times 4; rewrite
2 x - 2*4
2 is common to both; rewrite
2(x - 4)

Put them both together
x^3-4x^2+2x-8 = (x^3 - 4x^2) + (2x -8)
= x^2 (x-4) + 2(x-4)

(x-4) is common to both; rewrite:
(x-4)(x^2 + 2)

Answer 3

not a dumb question. the two use distinction of cubes. For expressions A and B A^3 - B^3 = (A - B)(A² + AB + B²). there's an identical sum of cubes formula A^3 + B^3 = (A + B)(A² - AB + B²). they're so comparable, it is trouble-free to bear in suggestions the two in case you bear in suggestions a minimum of one. So, to your first occasion----A = x and B = 3 x^3 - 27 = (x - 3)(x² + 3x + 9).

Answer 4

x^2(x - 4) - 2(x - 4)

(x^2 - 2)(x - 4)